If we assume that there is no connection between the age and gender, then we don't get any new information from knowing that the person is a man. So the question becomes "what is the probability that a person is between 60-69 years old" which is 42/290.
To see this, note that the probability that a random man is 60-69 years old, is the same as the probability that a random person is 60-69 years old, conditioned on that person being a man.
By the definition of conditional probability, we have
P(60-69|Man) = P(60-69 and Man)/P(Man)
Assuming that the age and gender of a person are independent, we get
P(60-69|Man) = P(60-69)*P(Man)/P(Man)
= 42/290 ~ 14.48%.